Load attenuating passively adaptive wind turbine blade

ABSTRACT

A method and apparatus for improving wind turbine performance by alleviating loads and controlling the rotor. The invention employs the use of a passively adaptive blade that senses the wind velocity or rotational speed, and accordingly modifies its aerodynamic configuration. The invention exploits the load mitigation prospects of a blade that twists toward feather as it bends. The invention includes passively adaptive wind turbine rotors or blades with currently preferred power control features. The apparatus is a composite fiber horizontal axis wind-turbine blade, in which a substantial majority of fibers in the blade skin are inclined at angles of between 15 and 30 degrees to the axis of the blade, to produces passive adaptive aeroelastic tailoring (bend-twist coupling) to alleviate loading without unduly jeopardizing performance.

GOVERNMENT RIGHTS

The Government has rights to this invention pursuant to Contract No.DE-AC04-94AL85000 awarded by the U.S. Department of Energy.

BACKGROUND OF THE INVENTION

1. Field of the Invention (Technical Field)

The present invention relates to rotor blades, particularly wind turbinerotor blades, and specifically to an aeroelasticly tailored turbineblades.

2. Background Art

Whenever the blades on a wind turbine are twisted, the twist directlyinfluences the blade's angle of attack, thereby changing loads andaffecting output power. Classic pitch control used in not only windturbines, but in rotors of all types, directly exploits theseprinciples. When the pitch changes are sufficiently rapid, they canaffect not only average rotor loads and turbine power, but vibratoryloads as well, influencing fatigue life throughout the system. Evenquite small angles of twist can have significant impact.

The general concept of rotor blades that passively adapt to the incidentwind loading is not new. Mechanisms that adjusted blade angle of attackin response to the thrust loading were quite popular in the early daysof the modem wind energy push of the late twentieth century. Approachesand objectives were quite varied. One effort regulated power with acentrifugally loaded mass on an elastic arm. Cheney, M. C. andSpeirings, P. S. M. (1978) “Self Regulating Composite Bearingless WindTurbine,” Solar Energy, Vol. 20. Another attempt employed a system forcyclically adjusting pitch for per rev load balancing. Bottrell, G. W.(1981) “Passive Cyclic Pitch Control for Horizontal Axis Wind Turbines,”Proceedings of Wind Turbine Dynamics, NASA Conf. Pub. 2185, DOE Pub.CONF-810226, Cleveland, Ohio. The North Wind 4KW had a system forpassively adjusting pitch for both power and load control. Currin, H.(1981) “North Wind 4kW ‘Passive’ Control System Design,” Proc. WindTurbine Dynamics, NASA Pub. 2185, DOE Pub. CONF-810226, Cleveland, Ohio.Others have studied alleviating yaw loads with cyclic pitch adjustments.Hohenemser, K. H. and Swift, A. H. P. (1981) “Dynamics of anExperimental Two Bladed Horizontal Axis Wind Turbine with Blade CyclicPitch Variation,” Wind Turbine Dynamics, NASA Pub. 2185, DOE Pub.CONF-810226, Cleveland, Ohio.

Also, a Garrad-Hassan report, for example, evaluated the use of allavailable blade loads to effect pitch changes that would regulate thepower output of a turbine, aiming at a flat power curve in high winds.Corbet, D. C. and Morgan, C. A. (1992) “Report on the Passive Control ofHorizontal Axis Wind Turbines,” ETSU WN 6043, Garrad Hassan andPartners, Bristol, UK, But only pitching to feather was evaluated toavoid the vagaries of predicting power output in the post-stall regime.The conclusion was that perfect regulation is very difficult to achieve,and that even less than perfect regulation is a challenge.

Regarding the construction of passively adaptive blades, Karaolis et al.introduced the concept of using biased lay-ups in blade skins on thesurface of blades to achieve different types of twist coupling for windturbine applications. By changing the blade skin surface from anorthotropic to a biased fiber lay-up, the blade can be aeroelasticallytailored with minimal disturbance to the beam stiffness properties ormanufacturing costs. Karaolis suggested that in addition to using theflapwise or centrifugal loading to twist a blade, it might be useful tointernally pressurize a spar and use changes in the pressure to activelycontrol the angle of blade twist. Karaolis, N. M., Mussgrove, P. J., andJeronimidis, G. (1988) “Active and Passive Aeroelastic Power Controlusing Asymmetric Fibre Reinforced Laminates for Wind Turbine Blades,”Proc. 10^(th) British Wind Energy Conf., D. J. Milbrow Ed., London,March 22-24, 1988; Karaolis, N. M., Jeronimidis, G., and Mussgrove, P.J. (1989) “Composite Wind Turbine Blades: Coupling Effects and RotorAerodynamic Performance,” Proc., EWEC'89, European Wind Energy Conf.,Glasgow, Scotland, 1989. FIG. 1.1 from the prior art shows how differentfiber orientations in a blade skin can be used to acheive bend-twist orstretch-twist coupling. In his 1988 report, Karaolis mapped out thecombinations of two direction lay-ups to maintain strength and producetwist coupling in an airfoil shape.

Middleton et al. and Infield et al.designed, analysed, fabricated andtested a “stretch- twist coupled” blade developed to control the rotorin a runaway scenario. Their composite blade was fabricated using ahelical layup with layers of glass and carbon fibers. Measured twistcoupling agreed well with predictions and measured runaway speeds wereactually less than predicted. Middleton, V., Fitches, P. Jeronimidis, G.and Feuchtwang, J. (1998) “Passive Blade Pitching for Overspeed Controlof an HAWT,” Wind Energy 1998, Proceedings of the 20^(th) British WindEnergy Association Conference, Cardiff University of Wales, Sep. 2-4,1998; Infield, D. G., Feuchtwang, J. B. and Fitches, P. (1999)“Development and Testing of a Novel Self-Twisting Wind Turbine Rotor,”Proceedings of the 1999 European Wind Energy Conference, pp 329-332,Nice, France, Mar. 1-5, 1999.

Another report on aeroelastic tailoring concluded that the use ofaeroelastic tailoring of the Fibre Reinforced Plastics to controllimited torsional deformation is a promising way to improve rotor bladedesign. Kooijman evaluated building the elastic coupling into the bladeskin. Some of his conclusions for blades designed for the “Smart Rotor”were that: (1) Bending-twist coupling gives the potential for a fewpercentages of energy yield improvement for constant-speedpitch-controlled turbines and improves starting torque by 10%; (2)Optimal constant-speed pitch-controlled rotor production is obtainedwith the inboard span twisting to feather and the outboard 60% of thespan twisting toward stall as wind speed increases; (3) The coupling isbest achieved with hybrid carbon/glass reinforcement in the cross plydirection; and (4) Bending-torsion flexibility is about 10% less than astandard construction. Kooijman, H. J. T. (1996) “Bending-TorsionCoupling of a Wind Turbine Rotor Blade,” ECN-I 96-060, NetherlandsEnergy Research Foundation ECN, Petten the Netherlands.

For constant speed rotors, enhanced stall control of wind turbines hasbeen used in the past to improve the energy capture of rotors byallowing the rotor size to grow while maintaining a low maximum ratingon other components in the system. Families of airfoils have beenpublished that have since been used to stall regulate turbines at lowerpower levels with the associated reduced system cost of energy. Tangler,J. and Somers, D. (1995) “NREL Airfoil Families for HAWTs,” Proc.Windpower '95, American Wind Energy Association, Washington D.C.;Klimas, P. C. (1984) “Tailored Airfoils for Vertical Axis WindTurbines,” SAND84-1062, Sandia National Laboratories, Albuquerque,N.Mex. An aeroelastically tailored blade that twists to stall inresponse to flap loads has a similar effect.

We have examined previously the generic coupling effects on annualenergy production of a nominally 26 meter diameter stall regulated windturbine. The blades were assumed to twist to stall, reducing maximumpower. The rotor diameter was then increased to bring maximum power backup to its initial level. Twist distributions were specified byprescribing a maximum tip amplitude and a spanwise variation, varyingwith wind speed in either a linear or quadratic fashion. A twistproportional to power was also used. It was discovered that the detailsof spanwise variation or how the twist varied with wind speed (or power)had only minor impacts. The twist-coupled blades combined with largerrotors increase power in the important middle-range of wind speeds whilepower in high winds remains the same. Studies which investigated theincrease in annual energy as a function of the annual average wind speedshowed that for a maximum twist angle of one degree the energy captureis increased by about 5% and for two degrees, about 10%. Theimprovements are not overly sensitive to the wind resource. Lobitz, D.W., Veers, P. S., and Migliore, P. G. (1996) “Enhanced Performance ofHAWTs Using Adaptive Blades,” Proc. Wind Energy '96, ASME Wind EnergySymposium, Houston Tex., Jan. 29 -Feb. 2, 1996, the disclosure of whichis incorporated herein by reference.

Whenever the wind turbine blade becomes aeroelastically “active,” thatis, the elastic deformations play a role in the aerodynamic loading,dynamic stability will be affected. We previously have addressed two ofthe most common stability constraints, namely classical flutter anddivergence. Classical flutter is the condition where the phasing betweenthe aerodynamic load fluctuations and elastic deformations are such thata resonant condition is achieved. Every wing will have a flutterboundary at some speed; for wind turbines the boundary is defined at therotational speed (typically determined in still air) at which the bladewill flutter. The stability margin is the difference between the flutterspeed and normal operating speed. Divergence is a quasi-static conditionwhere the blade twists in response to increasing load in a directionthat further increases the load. If this condition exists on a bladethere will be an operating speed at which the increase in loads causedby the deformation exceeds the ability of the blade to resist the load,called divergence. Lobitz, D. W. and Veers, P. S. “Aeroelastic Behaviorof Twist-Coupled HAWT Blades,” AIAA-98-0029, Proc. 1998 ASME Wind EnergySymposium held at 36^(th) AIAA Aerospace Sciences Meeting andExhibition, Reno, Nev., Jan. 12-15, 1998, the disclosure of which isspecifically incorporated herein by reference.

The stability boundaries were determined with respect to the amount oftwist coupling built into the blade. A coupling coefficient, α, whichvaries between -−and 1, was defined to facilitate the genericexamination of stability effects. For a blade with bending-twistcoupling, and prescribed bending and twisting stiffnesses, thiscoefficient represents a range for the coupling stiffness wherein thesystem remains positive definite.

Creating a bending twist/coupled finite element model of the 10 meterdiameter NREL Combined Experiment Blade for use in the MSC NASTRANcommercial software, the flutter and divergence stability boundarieswere mapped over the range of possible α's. Instability occurs when thedesign operating speed exceeds these boundaries. Results indicate thatthe stability boundaries are not exceeded even with coupling levels upto 80% of the theoretical maximum, although the stability marginsdecrease toward the extreme values of the coupling coefficient. As αbecomes increasingly positive, the blade bends and twists toward stall,increasing angle of attack and also loads, and this reduces thedivergence stability margin. Conversely, as α becomes increasinglynegative, the blade twists toward feather reducing aeroloads andincreasing the divergence stability margin. However, in this region, theclassical flutter stability margin decreases, although not as severelyas the divergence margin for positive α's. Lobitz, D. W. and Veers, P.S. (1998) “Aeroelastic Behavior of Twist-Coupled HAWT Blades,”AIAA-980029, Proc. 1998 ASME Wind Energy Symposium held at 36^(th) AIAAAerospace Sciences Meeting and Exhibition, Reno, Nev., Jan. 12-15, 1998.

Twisting to feather in response to increasing winds is a known potentialmeans to reduce the dynamic loading on the blades, and hence the rest ofthe system. Load reductions have been demonstrated by linking a pitchcontrol system to flapwise blade loads using simple integral control.Eggers, A. J. Jr., Ashley, H., Rock, S. M., Chaney, K., and Digumarthi,R. (1996) “Effects of Blade Bending on Aerodynamic Control ofFluctuating Loads on Teetered HAWT Rotors,” J. of Solar Energy Engr.,Vol. 118, No. 4, November 1996. Eggers' results indicated that the rmsblade bending response to turbulent winds could be reduced by abouthalf. And this was accomplished with rms pitching angles of 3 degrees if⅓ span ailerons are used and substantially less with full-span pitchcontrol. The fatigue implications of such a substantial decrease incyclic loading are enormous, measured in increased lifetime or reducedblade weight.

An aeroelastically twisting blade is similar to the control systeminvestigated by Eggers in that the blade pitch angle responds to bendingloads in a way similar to a proportional, rather than an integral,controller. The ability of bending-twist coupled blades to attenuate (orexacerbate) the cyclic loading was previously investigated for a 33meter diameter rotor employing three different control strategies;constant speed stall-controlled, variable speed stall- controlled andvariable speed pitch-controlled. Transient structural dynamicsimulations of the bending twist/coupled rotor were carried out usingthe ADAMS commercial software modified to include twist/coupling.Ensembles of 10 minute turbulent wind histories were generated with theSNLWIND-3D software and used to drive the rotor. Average windspeeds of8, 14 and 20 m/s (peak power for stall-control occurs near 17 m/s andfor pitch-control near 12 m/s) were investigated for both high and lowturbulence intensities. Material damage exponents of 3, 6 and 9 wereused for computing damage. Lobitz, D. W. and Laino, D. J. “LoadMitigation with Twist-Coupled HAWT Blades,” Proc. 1999 ASME Wind EnergySymposium held at 37^(th) AIAA Aerospace Sciences Meeting andExhibition, Reno, NV, Jan. 11-14, 1999, the entire disclosure of whichis hereby incorporated by reference.

Results for the constant speed stall-controlled case indicated thattwist/coupling toward stall produces significant increases in fatiguedamage, and for a range of wind speeds in the stall regime apparentstall flutter behavior is observed. For twist-coupling toward featherwith a coupling coefficient of magnitude, 0.6, fatigue damage isdecreased by 20 to 70% with the higher percentages occurring at thelower average windspeeds. Concurrent with lower fatigue damage estimatesfor twist-coupling toward feather, maximum loads decreased slightly,especially for the lower average windspeeds. For the case where thepitch offset is altered to bring the power curve of the twist coupledrotor into better agreement with that of the uncoupled one, differencesin average power are minimal. Lobitz, D. W. and Laino, D. J. “LoadMitigation with Twist-Coupled HAWT Blades,” Proc. 1999 ASME Wind EnergySymposium held at 37^(th) AIAA Aerospace Sciences Meeting andExhibition, Reno, Nev., Jan. 11-14, 1999.

There are limits to the amount of coupling that can be achieved withasymmetric fiber lay-ups. The best direction and the maximum couplingare a function of the fiber and matrix properties. Previous efforts haveindicated that stiffer fiber materials result in the higher couplingcoefficients, with maximum α for flat plates just below 0.8 for agraphite-epoxy system and 0.6 for a glass-epoxy system. The carbonsystem achieves maximum coupling with all the fibers at about 20 degreesto the axis of bending while the glass maximum is at about 25 degrees.Tsai, S. and Ong, C-H. (1998), “D-Spar Blade Design and Manufacture,”unpublished contractor reports, Sandia National Laboratories contractBB-6066 Stanford University. Composite, uniform, D-spars have beendesigned and fabricated that possess coupling coefficients in the rangeof 0.6. Ong, C. H. and Tsai, S. W. “Design, Manufacture and Testing of aBend- Twist D-Spar,” Proceedings of the 1999 ASME Wind Energy Symposium,Reno, Jan. 11-14, 1999, the teaching of which are hereby incorporated byreference.

There have been publicized efforts to develop a special twist/axialcoupled spar that will rotate a tip mechanism through large enoughangles to control power and provide some over. speed protection. Joose,P. A. and van den Berg, R. M. “Development of a TenTorTube for Blade TipMechanisms,” P7.17, Proc., 1996 European Union Wind Energy Conf. andExhib., Götegorg, May 20-24, 1996; van den Berg, R. M., P. A. Joosse,and B. J. C. Visser “Passive Power Control by Self Twisting Blades,”Proc., European Wind Energy Association Conf. and Exhib., Thessaloniki,Oct. 10-14, 1994.

There also have been showings of how small turbines can have improvedspeed regulation with twist/axial coupling. Infield D. G. and J. B.Feuchtwang “Design criteria for passive pitch control of wind turbinesusing self-twisting blades,” International Journal of Ambient Energy,Vol. 16, No. 3, July 1995; Feuchtwang, J. B. and D. G. Infield “Aerofoilprofile section for passive pitch control using self-twisting blades,”Wind Energy Conversion, Proc. 17^(th) BWEA Wind Energy Conf., ed. J.Halliday, BWEA, Warwick, Jul. 19-21, 1995. A common feature in theseworks is to provide relatively large rotations to achieve substantialamounts of power regulation. Most have used stretch twist coupling onvariable speed systems to assist in over-speed control or powerregulation and rely on large angles of twist to accomplish completecontrol of high wind loads.

And it has been demonstrated that even with relatively small twists(that incidentally also enhance regulation), a stall controlled, fixedpitch system could be operated with a larger rotor to achieve net energyenhancements without increasing the maximum power rating. Lobitz, D. W.,Veers, P. S., and Migliore, P. G. “Enhanced Performance of HAWTs UsingAdaptive Blades,” Proc. Wind Energy '96, ASME Wind Energy Symposium,Houston, Jan. 29 -Feb. 2, 1996.

The reorientation of the fiber directions in the rotor blade surfaceskin or spar to achieve either flap-load or extension-load coupling withblade twist, thus has potential to be a cost effective and reliableaeroelastic tailoring approach. The present invention involves modestblade rotations produced by elastic twist coupling of the blade as itbends or extends without any additional mechanisms or devices. There area number of possible uses of aeroelastic tailoring in wind turbineapplications. They include stall enhancement to permit larger diameterrotors for improved average energy capture, dynamic effects includingstability issues, and load alleviation through twist coupling towardfeather. In the present invention, the use of elastic twist coupling inthe rotor blade is exploited to alleviate loads to promote structurallongevity.

The present invention exploits modest twist angles to produce loadalleviation and perhaps power regulation or enhancement throughbend/twist coupling. The manufacturing process will depend on the typeof coupling to be produced. Fiber winding is well suited to producingstretch-twist coupling in a spar, while clam-shell construction with thetop and bottom skins manufactured separately is best suited tobend-twist coupling.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated into and form a partof the specification, illustrate several embodiments of the presentinvention and, together with the description, serve to explain theprinciples of the invention. The drawings are only for the purpose ofillustrating a preferred embodiment of the invention and are not to beconstrued as limiting the invention. In the drawings:

FIG. 1 is a diagram from the prior art, showing the types of asymmetricfiber lay-ups on rotor blades required to produce bending-twist andtension-twist coupling;

FIG. 2.1 is a line graph showing a ADAMS/NASTRAN comparison for theCombined Experiment Blade with bending-twist coupling, with tip flapdisplacement a function of the fraction of available coupling;

FIG. 2.2 is a line graph showing power curves (power as a function ofwind speed) for four models according to the present invention, showingthe effect of twist-coupling and pitch angle on power;

FIG. 2.3 is a line graph of turbulence intensity of simulated turbulencecompared to International Electrotechnical Commission standard criteria;

FIGS. 2.4(a)-(c) are bar graphs illustrating comparisons of relativefatigue damage for six blade models according to the present invnetion,and three material exponents for 100 simulated minutes, at (a) 8, (b)14, and (c) 20 m/s average wind speeds with the InternationalElectrotechnical Commission turbulence intensity;

FIGS. 2.5(a)-(c) are bar graphs illustrating comparisons of relativefatigue damage for six blade models according to the present inventionand three material exponents for 100 simulated minutes at (a) 8, (b) 14,and (c) 20 m/s average wind speeds with 50% of the InternationalElectrotechnical Commission turbulence intensity;

FIG. 2.6 is a line graph depicting a time series plot of blade bendingmoment showing the instability at coupling coefficient α=−0.6;

FIG. 2.7(a) and (b) are coefficient of lift plots showing that the rangefor 8 m/s (solid black squares) is greater than that for 14 m/s (opengray circles) for the low turbulence case (a), and both are smaller thanfor the 14 m/s high turbulence case (b), for model blades according tothe present invention.

FIG. 2.8 is a graph showing comparisons of cycle counted out-of-planebending moments at 14 ms average wind speed with InternationalElectrotechnical Commission turbulence intensity;

FIG. 2.9 is a bar graph comparing maximum out-of-plane moments over allsimulations for all models of the inventive blade and wind speeds;

FIG. 2.10 is a line graph comparison of curves of probability ofexceedence in ten minutes at 20 m/s average wind speed and associatedsimulation data points for maximum out- of-plane moment for all six windturbine models of the inventive blade;

FIG. 2.11 is a bar graph comparing average rotor power over allsimulations for all models of the inventive blade and wind speeds;

FIG. 3.1 is a line graph comparing pretwist for the twist-coupledinventive blades and uncoupled blades;

FIG. 3.2 is a line graph plotting the power curves for the uncoupledrotor and the twistcoupled inventive blade with optimal pretwist;

FIG. 3.3 is a line graph plotting power curves for a variable speedstall-controlled rotor with uncoupled rotors and a twist-coupledinventive rotor blade with optimal pretwist;

FIG. 3.4 is a line graph plotting power curves for a variable speedpitch-controlled rotor with uncoupled blades and a twist-coupled bladeaccording to the invention with optimal pretwist;

FIG. 3.5 is a graph plotting comparative C_(p) curve families for rotorspeeds from 12 to 36 RPM for the twist-coupled rotor according to thepresent invention and uncoupled rotors;

FIG. 3.6 is a graph comparing the efficiencies of the twist-coupledrotors according to the present invention and uncoupled rotors;

FIG. 3.7 is a line graph comparing the max efficiency RPM schedules forthe twist- coupled rotors according to the present invention anduncoupled rotors;

FIG. 3.8 shows bar graphs of the damage fractions for the baselineconstant speed stall-controlled controlled rotor;

FIG. 3.9 shows bar graphs of the damage fractions for a variable speedstall-controlled rotor;

FIG. 3.10 shows bar graphs of the damage fractions for a variable speedpitch- controlled rotor;

FIG. 3.11 shows bar graphs of power fractions for the twist-coupledrotor according to the present invention with three stall-controlstrategies;

FIG. 3.12 shows histograms of tip displacements for uncoupled,twist-coupled and softened uncoupled rotors at (14m/s, 100%International Electrotechnical Commission turbulence intensity); and

FIG. 3.13 shows bar graphs of damage fractions for a variable speedstall-controlled softened uncoupled rotor.

DESCRIPTION OF THE PREFERRED EMBODIMENTS (BEST MODES FOR CARRYING OUTTHE INVENTION)

Whenever wind turbine blades twist, there is a direct influence on theangle of attack, changing loads and affecting output power. This isdirectly exploited in classic pitch control used in not only windturbines but in rotors of all types. When the pitch changes are rapidenough, they can affect not only average loads and power, but vibratoryloads as well, influencing fatigue life throughout the system. Evenquite small angles of twist can have significant impact.

Broadly described, the present invention is a method and apparatus forimproving wind turbine performance by alleviating loads and controllingthe rotor. The invention employs the use of an passively adaptive bladethat senses the wind velocity or rotational speed, and accordinglymodifies its aerodynamic configuration. The passive approach is muchmore attractive due to its simplicity and economy. As an example, ablade design might employ coupling between bending and/or extension, andtwisting so that, as it bends and extends due to the action of theaerodynamic and inertial loads, it also twists modifying the aerodynamicperformance in some way. Thus, the invention exploits the loadmitigation prospects of a blade that twists toward feather as it bends.Stall regulation is more difficult if not impossible with the blade, andtherefore some other means of regulating the maximum power output of agiven sized rotor is recommended. One possibility is variable speedoperation which is becoming increasingly more popular with wind turbinedesigners. The invention includes passively adaptive wind turbine rotorsor blades with currently preferred stall-control features.

Wind turbines must operate in the presence of atmospheric turbulencewhich results in cyclic loads that fatigue the structure and produceextreme loads requiring high structural strength. As mentioned,traditionally no attempts have been made to reduce those loads throughaeroelastic tailoring, and only recently has aeroelastic tailoring evenbeen considered as a mode of improving turbine blade performance. In thecurrent invention, a composite fiber horizontal axis wind-turbine blade,in which a substantial majority of fibers in the blade skin are inclinedat angles of between 15 and 30 degrees to the axis of the blade,produces passive adaptive aeroelastic tailoring to alleviate loadingwithout unduly jeopardizing performance.

The top and bottom fibers are inclined in the same direction, eachproducing a “mirror” image of the other, thus presenting a“herring-bone” pattern at the leading edge of the blade. Thisinclination results in twist/flap coupling, i.e. a load that bends theblade in the flap direction will also induce a twist deflection. Theorientation of the coupling is such that an increasing upward flapdeflection results in a nose-down twist. General concepts andmethodologies for constructing twist-coupled rotor blades are describedat, for example, in Karaolis, N. M., Mussgrove, P. J., and Jeronimidis,G. “Active and Passive Aeroelastic Power Control using Asymmetric FibreReinforced Laminates for Wind Turbine Blades,” Proc. 10^(th) BritishWind Energy Conf., D. J. Milbrow Ed., London, Mar. 22-24, 1988;Karaolis, N. M., Jeronimidis, G., and Mussgrove, P. J. “Composite WindTurbine Blades: Coupling Effects and Rotor Aerodynamic Performance,”Proc., EWEC'89, European Wind Energy Conf., Glasgow, Scotland, 1989; andOng, C. H. and Tsai, S. W. “Design, Manufacture and Testing of aBend-Twist D-Spar,” Proceedings of the 1999 ASME Wind Energy Symposium,Reno, Jan. 11-14, 1999 (directed and sponsored by the assignee of thepresent application).

Such coupling in the rotor blade apparatus according to the inventionresults in attenuation of dynamic loads such that the cycling loadingdue to turbulence is reduced in all circumstances, and the extreme loadsdue to operation in turbulence are also reduced. This reduced cyclicloading extends the fatigue life of the blade as well as the other loadbearing structures in the turbine apparatus. The inventive blade isdesigned with extra twist while unloaded such that when the blade isoperated in winds near peak desired efficiency, the blade has untwistedunder load to a traditionally optimal twist distribution. As thefollowing examples illustrate by sophisticated modeling, loadattenuation has been found to occur in every situation of bladeoperation and turbulence level. Maximum load attenuation is attained onwind turbines where power regulation is achieved with pitch-controlledoperation in high winds.

Industrial Applicability

The invention is further illustrated by the following non-limitingexamples, wherein computer simulations were employed to model thebehavior of the inventive rotor blade.

Example 1

The analysis for the bending-twist coupled blade according to theinvention was carried out within the confines of beam finite elementtheory. The coupling terms for the beam elements are generated startingwith beam “stress- strain” relations. For bending-twist coupling the“stress-strain” relations at a point along the blade span are given byEquation 1: ${\begin{bmatrix}{EI} & {- g} \\{- g} & {GK}\end{bmatrix}\begin{bmatrix}\frac{\partial\theta}{\partial x} \\\frac{\partial\phi}{\partial x}\end{bmatrix}} = \begin{bmatrix}M_{b} \\M_{t}\end{bmatrix}$

Here, θ=δυ/δx is the flapwise slope of the blade, υ is the flapwisedisplacement, M_(b) is the flapwise bending moment, ψ is the bladetwist, and M_(t) is the twisting moment. The material parameters E and Gare the Young's modulus and the shear modulus respectively; I representsthe moment of inertia of the cross section and K the torsional moment ofinertia (equal to the polar moment of inertia for circular sections).The quantity g, is the coupling term, and has a value of zero for thestandard beam where no coupling is present. In order for this system tobe positive definite (i.e., the determinant of the matrix of Equation 1must be greater than zero) g is taken to be:

g=α{square root over (EIGK)}

where

−1<α<1

The coupling coefficient, α, provides for variable coupling within thedesignated limits. Past experience suggests that α may be limited to−0.6<α<0.6. Ong, C. H. and Tsai, S. W. (1999) “Design, Manufacture andTesting of a Bend- Twist D-Spar,” Proceedings of the 1999 ASME WindEnergy Symposium, Reno, Jan. 11-14, 1999. Only bending in the flapwisedirection is accounted for in Equation 1 above. Bending in the edgewisedirection is considered to be small relative to the flapwise direction,yielding minimal coupling. Axial extension is also ignored for this typeof coupling.

The example was implemented using ADAMS/WT and ADAMS/SOLVER software,which are commercially available from Mechanical Dynamics, Inc., of AnnArbor, Mich. In order to use the ADAMS/WT software (see ADAMS/WT User'sGuide, Version 1.50, February 1997) to create rotor models forsubsequent analysis with ADAMS (ADAMS/SOLVER Reference Manual, 1994)coupled with AERODYN (see Hansen, A. C. (1998) AeroDyn for ADAMS User'sGuide, Version 11.0, University of Utah, Salt Lake City, Aug. 31, 1998),modifications to incorporate the coupling in the “tapered beam”stiffness matrix were required. These modifications involved replacingthe k₄₆ and k₄ elements of the matrix, which are normally zeroed, withthe expression given below:$\overset{\_}{\frac{- {( {\alpha_{L} + \alpha_{0}} )\lbrack {( {{EI}_{L} + {EI}_{0}} )( {{GK}_{L} + {GK}_{0}} )} \rbrack}^{\frac{1}{2}}}{4L}}$

The subscripts L and 0 refer to the quantities evaluated at either endof the element. Further explanation of the other parameters in thisexpression can be found in the ADAMS/WT User's Guide. The couplingcoefficient parameter α was also added to the “Rotor Blade Data File” tofacilitate model input and provide for a coupling coefficient thatvaries with blade span. The above expression provided a mean value forthe coupling in each blade element. As the mean value is only exact forthe case of a uniform blade, the positive definiteness of the stiffnessmatrix may not be preserved for non-uniform blades with high absolutevalues of the coupling coefficient (e.g. |α|>0.9).

To verify that the coupling is incorporated in ADAMS/WT correctly,results for the Combined Experiment Blade (CEB) reported by us in“Aeroelastic Behavior of Twist-Coupled HAWT Blades,” AIAA-98-0029, Proc.1998 ASME Wind Energy Symposium held at 36^(th) AIAA Aerospace SciencesMeeting and Exhibition, Reno, Nev., Jan. 12-15, 1998, were reproducedwith ADAMS. These results are associated with the CEB turning in stillair over a range of bending-twist coupling levels. Blade tip rotationsand deflections are shown in FIG. 2.1 as a function of α for both thepreviously generated NASTRAN results and the current ADAMS results. Thefavorable agreement between the two provided confidence that the ADAMSmodeling was correct. Using a twist-coupled model of a representativestall-regulated rotor operating at a constant speed, ADAMS was exercisedusing stochastic wind time series generated with SNLWIND- 3D (seeKelley, N. D. (1993) “Full-Vector (3-D) Inflow Simulation in Natural andWind Farm Environments Using an Expanded Version of the SNLWIND (Veers)Turbulence Code,” Proceedings of the 12th ASME Wind Energy Symposium,Houston, 1993) for hub-height mean wind speeds of 8 m/s, 14 m/s and 20m/s. These wind speeds represent the linear aerodynamic, stall and poststall regions of the power curve, respectively.

Two turbulence levels were used in these example simulations, onerepresenting the current International Electrotechnical Commission (IEC)Class I standard and the other at 50% of that standard. These levelsrepresent a relatively turbulent and a relatively benign site,respectively. With these wind loadings, computations were completed forseveral values of the bending-twist coupling coefficient within a rangethat assured positive definiteness of the structural stiffness. Thesecoupling coefficients were α=−0.6, −0.3, 0.0, 0.3, and 0.6, with α=0.0corresponding to the uncoupled case. Load histories and power outputwere computed and stored for all of the above cases for subsequentprocessing.

Fatigue damage estimates were computed for these load histories assumingthat damage is proportional to the load cycle amplitude raised to amaterial exponent, b. The parameter b is often used to define thefatigue behavior of a material that follows the trend:$\overset{\_}{N \propto S^{- b}}$

where S is the stress amplitude and N is the number of cycles tofailure.

Values for b of 3, 6, and 9 were used to represent a range of materialsfrom welded steel to aluminum to composites. The damage is assumed to becumulative and therefor Miner's Rule was invoked. Damage results for thevarious levels of bending-twist coupling were compared to the uncoupledcase. Average power levels and maximum load levels were also compared.

The rotor model created using ADAMS/WT employed fully flexible bladescomprised of 20 elements each. All other model parts andinterconnections were rigid. Parameters for the basic model arepresented in Table 1. The blade was based on an existing 15 m-bladedesign, modified only to include the twist-coupling. No attempt was madeto optimize this blade.

TABLE 1 Model Configuration Sumary. Parameter Value Number of blades 3Rotor configuration upwind Yaw configuration fixed Blade length 14.9 mRotor hub radius 1.5 m Rotor precone angle 0 deg Rotor radius 16.4 mRotor hub height 50.0 m Rotor tilt angle 0 deg Rotor rotational speed(constant) 32 rpm

Models were created in ADAMS/WT for each of the five twist-coupling, α,values recited earlier. The pitch angle of the majority of these modelswas a constant 0.0 degrees. Power curves for three of these models areshown in FIG. 2.2. Because α affects blade twist and therefore stall, italso affects the power curve for the model, as shown in FIG. 2.2. Anadditional model was created for α=0.7 with a blade pitch of −4 degrees,to limit the peak power, and hence drivetrain loading, to that of theα=0.0 model. The power curve for this model is also shown in FIG. 5.2. Anoteworthy feature of the α=−0.6 power curve seen in FIG. 2.2 is theinstability near peak power (12-18 m/s), which apparently results fromthe onset of stall flutter.

Simulated turbulence was created using SNLWIND-3D for 3 average windspeeds as discussed earlier. Inputs to the program were chosen toduplicate conditions specified in the IEC standard. Shear velocity inputwas used to vary turbulence intensity. Ten 10-minute wind data sets werecreated at each wind speed for IEC turbulence intensity level, eachusing a different seed or initiation point for the random processutilized in generating the time series. Ten additional 10-minuteturbulence files were created at each wind speed with the turbulenceintensity set to 50% of IEC levels. FIG. 2.3 compares the turbulenceintensities of the simulated turbulence with the IEC criteria. In all, atotal of 100 minutes of simulated turbulence at each mean wind speed andturbulence level were created. Thus, with the six models investigated, atotal of 3600 simulated minutes—comprised of 360 10-minutesimulations—were used in the analysis.

Results demonstrated in the simulation included fatigue damage, averagepower and maximum load for the various cases. In addition to the damageestimates, sample load spectra are herein disclosed. A sample load timehistory is also included of interest to show the development of apossible stall flutter instability.

FIGS. 2.4(a), 2.4(b), and 2.4(c), and FIGS. 2.5(a), 2.5(b), and 2.5(c)summarize the fatigue damage for most of the simulations for a bladeaccording to the invention. FIG. 2.4 discloses the results for the highturbulence intensity corresponding to the IEC standard, while FIG. 2.5for half of that turbulence level. The damage was computed for theout-of-plane root bending moment only, since the loads were generallyhighest at that location. Loads due to blade twist were not consideredin the damage computation. For each turbulence intensity the damage wasnormalized to the damage that occurs for the 14 m/s wind speed andα=0.0. Thus in FIGS. 2.4 and 2.5b, the damage associated with the α=0.0bar is set to unity for all three values of the material exponent. Inall cases positive α indicates twisting toward feather, and negative α,toward stall.

Attention is invited to FIGS. 2.4(b) and 2.5(b). It is apparenttherefrom that twisting to stall dramatically increases fatigue damagefor the 14 m/s wind speed, probably as the result of an apparent stallflutter instability that occurs for negative α in the stall and poststall wind regimes. As mentioned, the power curve for α=−0.6 in FIG. 2.2shows a region of instability from approximately 12 m/s out to 18 m/ s.This instability is also apparent in the time series plot of FIG. 2.6for the out-of-plane moment. Here the frequency of the instability isapproximately 1.7, Hz which is close to the frequency of the firstbending-twist coupled mode of the α=−0.6 blade, as listed in Table 2.

TABLE 2 Non-Rotation Blade 1^(st) Flap Freqs {acute over (α)} −0.6 −0.30.0 0.3 0.6 Freq (hz) 1.69 2.25 2.39 2.22 1.65

For the 8 m/s and 20 m/s wind speeds, coupling toward stall stillcarried a high damage penalty, although not as dramatic as that for the14 m/s wind speed, where stall events occur more often. Thus, comparingdamage results for α=0.0 and α=0.6 (twisting toward feather), there wasat least a factor of two reduction in damage in almost all cases withsignificantly greater reductions for the 8 m/s wind speed. For the caseof α=0.3 the reductions in damage were proportionately much less thanfor those of α=0.6, especially for the 20 m/s wind speed. In general,the trend of reduced relative damage with increasing α was roughlyindependent of the material exponent.

FIGS. 2.5(a) and (b) show the result that the relative damage for b=6and 9 was greater for some α's at 8 m/s than at 14 m/s. This is due todifferences in the range of lift coefficient realized at different windspeeds and turbulence levels. For low turbulence, it was determined thatat 8 m/s the blade operated in the linear part of the lift curve,covering a range from 0.6 to 1.4. At 14 m/s, the blade operated in stalltransition covering the smaller range from 1.2 to 1.6. Therefore,although the loads were in general greater at 14 m/s, loads cycles wereactually larger at 8 m/s. Thus, the lift curve range for 14 m/s was muchgreater for the higher turbulence level—0.6 to 1.6 —than for the lowerturbulence level, hence this result of higher damage at lower wind speedis not evident in FIG. 24.

FIG. 2.8 shows load spectra for α =−0.6, 0.0, and 0.6 for the 14 m/saverage wind speed with IEC turbulence intensity. Cycle amplitudeclearly increases with decreasing α, and the effect of the instabilityfor α=−0.6 mentioned above is dramatic.

FIG. 2.9 provides comparisons of the maximum bending moments that occurin each time series for the various α's and average wind speeds. Foreach wind speed the maximum load for α=0.6 is somewhat less than thatfor α=0.0. The random nature of the turbulence, however, can make such adirect comparison of maximum values misleading. A preferable manner ofcomparing the maxima is using probability of exceedence curves. Thesewere calculated using a Gumbel distribution fit from the FITS routine(see Kashef, T. and Winterstein, S. R (1998) Moment Based Modeling andExtreme Response Estimation—The FITS Routine, Report No. RMS-31, CivilEngineering Dept., Stanford University, 1998), and are shown in FIG.2.10 for the 20 m/s case. It is clear that the probability of exceedinga given maximum load value tends to decrease with increasing α.

FIG. 2.11 shows the average power for the various cases and, except forthe average wind speed of 8 m/s, the average power is greater for α=0.6than for α=0. This result is consistent with the power curves of FIG.2.2. Thus, we have determined that for a blade that twists to feather asit bends, with a bending-twist coupling coefficient of α=0.6, the rotorproduces equivalent average power and simultaneously experiences smallermaximum loads and half the fatigue damage when compared to the uncoupledblade.

To obtain a more rigorous comparison, the blade pitch of theabove-described inventive twist-coupled rotor was adjusted toward stallto obtain a power curve similar to the curve for the uncoupled rotor.This was accomplished by setting the pitch of the twist-coupled rotor to−4.0 degrees. The resulting power curve, shown in FIG. 2.2, is inreasonable agreement with the one for the uncoupled rotor. As shown inFIG. 2.9, the maximum loads for the pitched blade rotor with α=0.7 creptup a little higher than those of the unpitched, α=0.6 model, and becameroughly equivalent to those for the uncoupled rotor. The probability ofexceedence for a given maximum load also increases slightly for thepitched blade as shown in FIG. 2.10. Similarly, as shown in FIG. 2.11,the average power levels have crept down some and are also roughlyequivalent to those for the uncoupled rotor. (This was expected sincethe two power curves are now roughly equivalent). However, referring toFIGS. 2.4 and 2.5 (a, b, and c), the fatigue damage levels for nearlyall cases shown were still shown to be reduced by at least a factor oftwo when compared to those of the uncoupled rotor. Thus in this case theprimary improvement provided by the inventive twist-coupled blade is asubstantial reduction in fatigue damage.

Thus, the ADAMS software was employed to confirm the feasibility ofusing blades that twist as they bend to mitigate fluctuating loads. Timeseries calculations were made for three average hub-height wind speeds,two wind turbulence settings and five levels of twist-coupling. Fatiguedamage was computed from the load histories using material exponentsthat represented materials ranging from welded steel to composites.

We determined that twist-coupling toward stall produces significantincreases in fatigue damage, and for a range of wind speeds in the stallregime apparent stall flutter behavior is observed. For twist-couplingtoward feather with a coupling coefficient of 0.6, however, fatiguedamage is decreased by at least a factor of two for almost all of thecases investigated. The damage reductions seemed to be relativelyindependent of the material exponent.

Concurrent with lower fatigue damage estimates for positivetwist-coupling, maximum loads decreased modestly and average powerincreased due to elevations in the power curve in the stall region. Whenthe pitch was altered to bring the power curve into agreement with thatof the uncoupled rotor, fatigue damage levels remained at the samereduced levels while differences in maximum load and average power arereduced.

The following example is of an inventive rotor blade which attenuatesloading while also addressing the added problem of power regulation.

Example 2

The present invention includes improved bending twist-coupled blades inrotors that use different power-control strategies. In confirming thesealternative embodiments, a constant speed type stall-controlled rotorwas included in the simulation as a baseline. Two of the more commonlyaccepted control strategies, variable speed stall-control and variablespeed pitch-control, were used. The blades of each of these alternativeembodiment rotors were first optimized mized by setting the pretwistsuch that a desirable twist distribution is achieved at rated power. Ineach case this procedure produced power curves for the twist-coupledrotors that were nearly identical to those of the uncoupled rotors towhich they were compared.

A separate study for the variable speed stall-controlled rotor wasperformed wherein the twist-coupled rotor efficiency was compared tothat of the uncoupled one in a steady wind environment. The peak rotorefficiency was determined at each windspeed by optimally adjusting therotor RPM. This peak efficiency was plotted versus wind speed andcompared to that for blades with no twist-coupling.

For the three rotors, simulations were completed for turbulent winds tocompare the associated fatigue damage reductions for the twist-coupledblades relative to the uncoupled ones. Power degradations were alsodetermined.

Because twist-coupling tends to soften rotor blades, additionalsimulations were completed to assess the degree to which this softeningalone reduces the fatigue damage. Thus, the variable speedstall-controlled rotor blades were softened to have the equivalentstiffness of the twist-coupled ones, but without the twist-coupling.

Using twist-coupled models of a representative rotor and three differentcontrol strategies, ADAMS was exercised using turbulent wind time seriesgenerated with NLWIND-3D for hub-height mean windspeeds of 8 m/s, 14 m/sand 20 m/s, each approximately 90 minutes in length. For thestall-controlled rotors, these windspeeds represented the linearaerodynamic, stall and deep stall regions of the power curve,respectively. Two turbulence levels were used in these simulations, thecurrent IEC Class I standard and 50% of that standard. As mentioned,these respective levels represent a relatively turbulent site and arelatively benign site, respectively. With the wind loadings defined asabove, computations were completed for blades with the optimal pretwistand a value of the bending-twist coupling coefficient of α=0.6, whereα=0.0 corresponds to the uncoupled case. Load histories and power outputwere computed and stored for all of the above cases for subsequent postprocessing.

Fatigue damage estimates were computed for these load histories assumingthat damage is proportional to the load cycle amplitude raised to amaterial exponent, b, namely:

D∝S^(b)

where S is the stress amplitude and D is fatigue damage.

Values for b of 3, 6, and 9 were used to represent a range of materialsfrom welded steel to aluminum to composites. Results are also presentedfor a value of b=1, which represents the average cyclic load. The damagewas assumed to be cumulative and therefore Miner's Rule again wasinvoked. Damage results for the selected level of bending-twist couplingwere compared to the uncoupled case. Average power levels were alsocompared.

The rotor models created using ADAMS-WT employed fully flexible bladescomprised of 20 elements each. All other model parts andinterconnections were rigid. Parameters for the basic model arepresented in Table 3. The rotor blade was based on an existing 15 mblade design, modified to include twist-coupling. Models were developedfor coupling coefficients of α=0.6 and α=0.0. For the uncoupled case,the pretwist varies as indicated in FIG. 3.1 by the solid curve (thenegative sign indicating twist toward feather). For the twist-coupledrotor the pretwist was set so that this twist distribution was achievedat rated power.

TABLE 3 Alternative Model Configuration Summary. Parameter Value Numberof blades 3 Rotor configuration upwind Yaw configuration fixed Bladelength 14.9 m Rotor hub radius 1.5 m Rotor precone angle 0.0 deg Rotorradius 16.4 m Rotor hub height 50 m Rotor tilt angle 0.0 deg Sling (distfrom yaw axis to 4.0 m hub) Rotor rotational speed 0-32 RPM (variable)

This pretwist was determined by building a rotor with two blades in thesame azimuthal location, one uncoupled and one with twist-coupling.Pointers in the ADAMS/Solver dataset were then modified so thataeroloads from AERODYN computed for the uncoupled blade were alsoapplied to the coupled one (in lieu of the aeroloads AERODYN wouldnormally compute for it). The blade twist distribution that occured dueto the twist-coupling under this loading was then subtracted from thedesired twist distribution providing the optimal pretwist. Thus, whenthe aeroelastic twists were included in the aeroload computations, thetwist distribution at the rated power coincided with the desired one.The accuracy of this technique depends, however, on the linearity of theblade twist with the aeroloads in the range of interest.

For the rotor turning at 32 RPM, the windspeed at rated power wasdefined to be 13 m/s. This value was selected in part to bring the peakpower of the twist-coupled rotor into compliance with the peak power ofthe uncoupled rotor. The optimal pretwist for the twist-coupled bladeunder the load associated with this windspeed is shown by the dashedcurve in FIG. 3.1. To be more consistent with convention, this pretwistcould be recast by shifting the distribution so that the pretwist iszero at the tip and then specifying a full blade pitch of 4.85 degreestoward stall.

The power curves for the coupled with optimal pretwist and uncoupledrotors operating at a constant speed of 32 RPM are shown in FIG. 3.2.The two power curves are essentially equivalent, with the uncoupledrotor generating slightly more power than the twist-coupled one at theextremes of the windspeed range. Variable speed operation was effectedby applying a reactive torque to the rotor at the low speed shaft. Forthe linear aerodynamics range of the power curve, this torque was madeproportional to the RPM squared with the coefficient selected to balancethe torque produced by the wind loads, thereby allowing the rotor tooperate at maximum efficiency. The coefficient for the torque equationin the linear range was computed using data from the peak of the C_(p)curve for the uncoupled rotor. This coefficient was also used for thetwist-coupled rotor although it may not be optimal.

For the variable speed stall-controlled rotor, a variable speedtransitions to the constant speed at 32 RPM. The tip speed ratio at peakC_(p), combined with this rotor speed, indicate that the correspondingwind speed for the onset of constant speed operation is approximately8.6 m/s. Constant speed operation was accomplished by significantlyincreasing the reactive torque when the RPM exceeds the desired constantspeed value. Power curves for the uncoupled rotor and the twist-coupledone are shown in FIG. 3.3, with the pretwist of FIG. 3.1 applied to thetwist-coupled blades. (FIG. 3.3 suggests that the coefficient in thetorque equation for variable speed operation is sub-optimal.)

For a variable speed pitch-controlled rotor, variable speed operationcontinues until peak power is achieved. This occurs at an RPM ofapproximately 43.5 RPM with a corresponding wind speed of 12 m/s. Forhigher wind speeds, the rotor speed is held at this value and power isalso held constant through active full span pitch control. Power curvesfor the uncoupled rotor and the twist-coupled one are shown in FIG. 3.4,with the pretwist of FIG. 3.1 applied to the twist-coupled blades.

Simulated turbulence was created using SNLWIND-3D for 2 average windspeeds as disclosed earlier herein. Inputs to the program were chosen toduplicate conditions specified in the IEC standard. Shear velocity inputwas used to vary turbulence intensity. Nine 10-minute wind data sets,each with a different seed, were created at each wind speed for IECturbulence intensity levels. Nine additional 10-minute turbulence fileswere created at each wind speed with the turbulence intensity set to 50%of IEC levels. Generally turbulence intensities for the simulated windsat 8, 14 and 20 m/s came out slightly less than the target values.

For an uncoupled variable speed stall-controlled rotor, the efficiencyof the rotor in the linear aerodynamic range can be maximized by runningat the tip speed ratio associated with the peak of the power coefficientcurve. For the twist-coupled case, however, the location of the peak ofthe power coefficient curve changes modestly with rotor RPM due to thetwisting of the blades. Thus the maximum rotor efficiency must berepresented as a function of windspeed (or RPM), and the RPM versuswindspeed schedule required to achieve maximum efficiency must bealtered from that of the uncoupled rotor.

Using the ADAMS software for both the twist- coupled and uncoupledrotors, power curves were generated for rotor speeds from 12 to 36 RPMin intervals of 3 RPM for windspeeds varying from 4 to 20 m/s. Thefamilies of C_(p) curves shown in FIG. 3.5 were developed from thesepower curves. For the uncoupled rotor, these curves are nearlycoincident as expected, but for the twist-coupled rotor there is somedegree of spread due to the induced blade twisting. Plots of the maximumefficiency versus windspeed shown in FIG. 3.6 were also developed fromthe power curves. These curves indicate that over a significant portionof the windspeed range associated with linear aerodynamics, the maximumrotor efficiencies are essentially identical. At lower windspeeds theuncoupled rotor operates at modestly higher efficiencies than thetwist-coupled rotor.

The RPM versus windspeed schedules required to achieve theseefficiencies are shown in FIG. 3.7. It is noted that the schedule forthe uncoupled rotor is approximately linear with windspeed, representinga constant tip speed ratio. The C_(p) curves of FIG. 3.7 indicate thatthose for the twist-coupled rotor tend to have sharper peaks than thosefor the uncoupled rotor. (This may make it more difficult for thetwist-coupled rotor to achieve maximum efficiency in a turbulent windenvironment, resulting in reduced energy capture.)

This disclosure includes normalized fatigue damage and average power foruncoupled and twist-coupled constant speed stall-controlled, variablespeed stall-controlled, and variable speed pitch-controlled rotorsdriven by the various turbulent wind loadings. The fatigue damage iscomputed for the out-of-plane root bending moment only as the loads aregenerally highest for that moment at that location. Loads due to bladetwist are not considered in the damage computation. FIG. 3.8 summarizesthe fatigue damage results for the baseline constant speedstall-controlled rotor. For each turbulence intensity and wind speed thedamage fraction which is the ratio of the damage incurred by thetwist-coupled rotor and the uncoupled one is set forth.

Although not immediately apparent from the damage fractions, themagnitude of the damage reductions is markedly greater for the highermaterial exponents, as indicated by the “log(Total Damage)” bar chart ofFIG. 3.8. Generally, the damage fractions run from 0.7 to 0.8, exceptfor the higher exponents at the 8 m/s average wind speed where they aresignificantly lower. This is the result of the higher load ranges thatoccur when the rotor is operating in the linear aerodynamic range,providing a greater opportunity for damage reduction. The damagefractions are generally smaller for 100% turbulence when compared to 50%turbulence. The bars for the material exponent of 1 signify the averagecyclic load fractions that occur for the twist-coupled rotor relative tothe uncoupled one. They are approximately 0.9 at 8 m/s and near 0.8 forthe higher wind speeds.

Fatigue damage results for the variable speed stall-controlled rotorshown in FIG. 3.9 are generally similar to those for the baselineconstant speed rotor presented in FIG. 3.8. For the variable speedpitch-controlled rotor, the damage fractions shown in FIG. 3.10 weregenerally lower than those for the previous two cases. At the averagewind speed of 8m/s, the results were similar to prior ones but for thehigher wind speeds the damage fractions were substantially smaller. Thisis a consequence of the pitch-control, which keeps the rotor operatingin the linear aerodynamic range regardless of wind speed. As for the 8m/s windspeed, the higher load ranges that occured when the rotoroperated in this range provided greater opportunity for damagereduction. Generally, but not always, the higher turbulence levelproduced smaller damage fractions.

In FIG. 3.11, power fractions, which are the ratio of the power producedby the twist-coupled rotor and the uncoupled one, are provided for thethree control strategies. As indicated, differences in power outputbetween the uncoupled and twist-coupled rotors are negligible for allthree control strategies.

Mathematical expressions have previously been presented indicating thatthe introduction of off diagonal terms in the beam stiffness matrix tomodel twist-coupling causes the beam to become softer in bending, eventhough the terms representing the flexural rigidity are not altered.Lobitz, D. W. and Veers, P. S. (1998) “Aeroelastic Behavior ofTwist-Coupled HAWT Blades,” AIAA-98-0029, Proc. 1998 ASME Wind EnergySymposium held at 36^(th) AIAA Aerospace Sciences Meeting andExhibition, Reno, Nev., Jan. 12-15, 1998; Ong, C. H. and Tsai, S. W.(1999) “Design, Manufacture and Testing of a Bend- Twist D-Spar,”Proceedings of the 1999 ASME Wind Energy Symposium, Reno, Jan. 11-14,1999. This softening was also apparent in the present simulations, whereblade tip deflections for the twist-coupled rotor exceed those of theuncoupled one by approximately 50%, as shown in the histograms of FIG.3.12 for the 14 m/s windspeed at 100% IEC turbulence intensity.

To determine the role this softening plays in the damage reduction, anadditional uncoupled model was developed where both the blade flexuralrigidity and torsional stiffness were reduced to be commensurate withthose of the twist-coupled model. Variable speed, stall control was usedto control the rotor. Resulting blade tip deflections for this model areequivalent to those of the twist-coupled rotor (see FIG. 3.12). Fatiguedamage comparisons for this softer uncoupled model, relative to theprevious uncoupled one, are shown in FIG. 3.13 using the damage fractiondefined as the ratio of the damage incurred by the softer uncoupledrotor and that of the original uncoupled one. The bar charts for the 8m/s windspeed show a damage reduction associated with the softeruncoupled model, although not as large as that of the twist-coupledrotor shown in FIG. 3.9. For 14 m/s windspeed where the rotor hasentered the stall aerodynamic range, the damage for the softer uncoupledrotor actually increases relative to the stiffer one. Thus, softeningthe blades produces mixed results with regard to fatigue damagereduction, and at best provides only a fraction of the damage reductionproduced when twist-coupling is incorporated.

We thus determined the feasibility of using inventive wind turbineblades that twist as they bend to mitigate fluctuating loads for avariable speed rotor. The twist coupling coefficient for the blades wasset at α=0.6 (twisting toward feather), and the blades were pretwistedtoward stall to match the constant speed power curve for uncoupledblades. Power control was achieved using three different strategies. Thefirst, used as a baseline, was just stall control with a constant speedrotor. In the second, variable speed was implemented by imposing areactive torque on the low speed shaft proportional to the RPM squaredwith the coefficient specified, so that the rotor operates at peakefficiency in the linear aerodynamic range, and, at higher wind speeds,by limiting the maximum RPM to take advantage of the stall controllednature of the rotor. The third strategy also employed variable speed,but pitch control was implemented at the higher wind speeds enabling therotor to continue operating in the linear aerodynamic range.

Prior to running turbulent wind simulations, steady wind results wereobtained showing that for variable speed stall-controlled operation thetwist coupled rotor described above can be almost as efficient as theuncoupled one if a slightly altered RPM versus windspeed schedule isfollowed.

Accordingly, turbulent wind simulations were made for three averagehub-height wind speeds and two wind turbulence settings. Fatigue damagewas computed from the load histories using material exponents thatrepresent materials ranging from welded steel to composites. In mostcases, significant fatigue damage reductions of from 20% to 80% wereexhibited by the twist-coupled rotor. For the constant speed andvariable speed rotors that employed stall-control, significant damagereductions were observed at the higher material exponents for the 8 m/saverage wind speed where the rotor operates primarily in the linearaerodynamic range. For the variable speed pitch-controlled rotor,significant reductions were observed at the higher wind speeds as welldue to its ability to continue to operate in the linear aerodynamicrange even at the higher windspeeds. In all cases power production forthe twist-coupled rotor was equivalent to the uncoupled one. Thus, forthe twist-coupled rotor, substantial fatigue damage reductions prevailedfor the rotor in variable speed operation as in the case for constantspeed, and with no loss in power output.

The preceding examples can be repeated with similar success bysubstituting the generically or specifically described reactants and/oroperating conditions of this invention for those used in the precedingexamples.

Although the invention has been described in detail with particularreference to these preferred embodiments, other embodiments can achievethe same results. Variations and modifications of the present inventionwill be obvious to those skilled in the art and it is intended to coverin the appended claims all such modifications and equivalents. Theentire disclosures of all references, applications, patents, andpublications cited above are hereby incorporated by reference.

What is claimed is:
 1. A passively adaptive horizontal axis wind-turbineblade comprising a top, a bottom, a tip and a principal axis, and saidblade comprising a composite fiber surface skin in which a substantialmajority of fibers in said skin are inclined at angles of between 15 and30 degrees to said axis, the fibers on said top and said bottom inclinedin the same direction, wherein upward flap deflection of said bladeinduces said blade to twist toward feather with a bend-twist couplingcoefficient of between 0.0 and 0.6.
 2. A wind turbine blade according toclaim 1 wherein said blade comprises a pretwist of zero at said tip andfull blade pitch of approximately 5 degrees toward stall.
 3. At leasttwo wind turbine blades according to claim 2 combined to comprise a windturbine rotor, wherein said rotor is stall-controlled at constant speed.4. At least two wind turbine blades according to claim 3 wherein each ofsaid blades manifests a damage fraction relative to an uncoupled bladeof less than 1.0.
 5. At least two wind turbine blades according to claim2 combined to comprise a wind turbine rotor, wherein said rotor ispitch-controlled at constant speed.
 6. At least two wind turbine bladesaccording to claim 5 wherein each of said blades manifests a damagefraction relative to an uncoupled blade of less than 1.0.
 7. At leasttwo wind turbine blades according to claim 2 combined to comprise a windturbine rotor, wherein said rotor is stall-controlled at variable speed.8. At least two wind turbine blades according to claim 7 wherein each ofsaid blades manifests a damage fraction relative to an uncoupled bladeof less than 1.0.
 9. At least two wind turbine blades according to claim2 combined to comprise a wind turbine rotor, wherein said rotor ispitch-controlled at variable speed.
 10. At least two wind turbine bladesaccording to claim 9 wherein each of said blades manifests a damagefraction relative to an uncoupled blade of less than 1.0.